Definitions of Geometric Terms

1. Definitions of Geometric Terms

2. Definitions • RAY: Defined as …Ray AB is part of line AB that contains Point A and all the points on line AB that are on the same side of point A as point B. Ray AB has an endpoint of A; B A Ray AB

3. Definitions Take Note! These are two different rays!

4. Definitions Name a ray in two ways.

5. Definitions • ANGLE:Two rays that share a common endpoint, provided that the two rays do not lie on the same line. The common endpoint of the two rays that make an angle is the vertex of the angle. The two rays are called the sides of the angle. Side How do we name angles? Side A Vertex A

6. Definitions • MEASURE OF AN ANGLE: • The smallest amount of rotation for a ray to move from the overlapping position to the final position • In DEGREES How do write an angle’s measure in symbol form? 28.6o 115o

7. Definitions • CONGRUENT: Two geometric figures are congruent if and only if they are identical in shape and size. 40o Are these congruent even if they point to different directions? 40o

8. Definitions • CONGRUENT ANGLES: Two angles are congruent angles if and only if they have the same measure. 40o 40o

9. Definitions • ACUTE ANGLE: An angle whose measure is less than 90o 30o 95o 50o 40o

10. Definitions • ACUTE ANGLE: An angle whose measure is less than 90o 60o 30o 95o 50o 40o Is the angle formed by 2 segments acute?

11. Definitions • RIGHT ANGLE: An angle whose measure is 90o 75o 40o 90o 90o 2 intersecting lines can form angles. 126o

12. Definitions • OBTUSE ANGLE: An angle whose measure is greater than 90o 30o 95o 130o 60o 155o 40o

13. Definitions • ANGLE BISECTOR: A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure. D A What ray bisects Angle ABC? 60o 60o B Ray BD. C E

14. Definitions • ANGLE BISECTOR: A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure. D Is the green ray an angle bisector of Angle ABE? A 60o 60o B No. The ray does not share the vertex of angle ABE. C E

15. Definitions • PARALLEL LINES: Two coplanar lines that do not intersect.

16. Definitions • COMPLEMENTARY ANGLES:Two angles whose measures have the sum of 90o. Pairs of Complementary Angles

17. Definitions • VERTICAL ANGLES:If Line AB and Line CD intersect at point P so that point P is between points A and B and also between points C and D, then APC and BPD are a pair of vertical angles. Angles APD and BPC are also a pair of vertical angles. D P A B C Common vertex

18. Definitions G F W P R S X B T H Pairs of Vertical Angles: G and R; W and P; X and T; S and H Are these pairs of Vertical Angles: B and F? Z and K? J and A? Z A J K

19. Definitions • PERPENDICULAR LINES: Two lines that intersect to form a right angle. Line J A right angle is an angle whose measure is 90 degrees. Therefore, perpendicular lines form angles of 90 degree measures. Line B

20. Definitions • PERPENDICULAR LINES: Two lines that intersect to form a right angle. 90o Are intersecting lines always perpendicular? Can we call the green segments as perpendicular segments? No.

21. Definitions • SUPPLEMENTARY ANGLES: Two angles whose measures have the sum of 180o. A M 95o 110o 70o D 85o G Pairs of Supplementary Angles 150o 30o

22. Definitions • LINEAR PAIR OF ANGLES:If X, Y, and Z are consecutive collinear points and W is a point not on Line XZ, then XYW and WYZ form a linear pair of angles. W X Y Z Collinear points

23. Definitions • LINEAR PAIR OF ANGLES:2 angles form a linear pair if they share the same vertex, share same sides, and whose non-shared sides form a line. Shared sides G H Non-Shared sides Non-Shared sides Common Vertex